Geometry parallel lines proofs worksheet

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If two lines which are parallel are intersected by a transversal then the pair of corresponding angles are equal. From Fig. 3: ∠1=∠6, ∠4=∠8, ∠2= ∠5 and ∠3= ∠7. The converse of this axiom is also true according to which if a pair of corresponding angles are equal then the given lines are parallel to each other.These geometry worksheets are a good resource for children in the 5th Grade through the 10th Grade. Parallel and Perpendicular Lines Worksheets This section contains all of the graphic previews for the Parallel and Perpendicular Lines Worksheets.Parallel lines are important in mathematics because they are at the base of several conjectures involving angles in geometry. Drawing a line, called a transversal, through a pair o...SaaS small businesses are facing challenging macroeconomic conditions once again. Here are 5 tips for recession-proofing your SMB. SaaS small businesses are facing challenging macr...Parallel Lines Proof Worksheet Name _____ Write a 2 column or flow proof on your own paper. 1. Given: l || m; ∠2 ≅ ∠4 2. ... Microsoft Word - Parallel Proofs.DOCThe symbol ∥ means “is parallel to.”. When a line intersects two or more lines, the angles formed at the intersection points create special angle pairs. A transversal is a line that intersects two or more coplanar lines at distinct points. The special angle pairs formed by parallel lines and a transversal are congruent, supplementary, or ...Geometry Worksheets Listed Alphabetically: Algebraic Representations. Analyzing in Three Dimensions. Angle Word Problems. Angles. Angles Circles- Chords. Angles Outside the Circle. Angles with Parallel Lines. Arcs in Circles. Proving Lines Parallel 134 Chapter 3 Parallel and Perpendicular Lines page 30 and Lesson 2-1 Algebra Solve each equation. 1. 2x +5 =27 11 2. 8a-12 =20 4 3. x-30 +4x +80 =180 26 4. 9x-7 =3x +29 6 Write the converse of each conditional statement. Determine the truth value of the converse. 5–6. See back of book. 5. If a triangle is a right ...

1.and have no points in common. and are parallel. 2.and have only one point in common. and intersect. 3.and have all points in common. and are the same line. These three possibilities can also be stated in the following postulate: Postulate 9.1Two distinct coplanar lines are either parallel or intersecting. CD.Mathster keyboard_arrow_up. Mathster is a fantastic resource for creating online and paper-based assessments and homeworks. They have kindly allowed me to create 3 editable versions of each worksheet, complete with answers. Worksheet Name. 1. 2. 3. Graphs - Parallel Lines. 1.THE (ULTIMATE) GEOMETRY REVIEW SHEET...WITH COMMON CORE GOODNESS. (2016 Edition) Some General Information. The Common Core Regents Exam Basics: Time: 3 hours Problems: 36. Part I: 24 multiple choice problems (2 pts each) = 48 pts Part II: 7 short answer problems (2 pts each) = 14 pts Part III: 3 short answer problems (4 pts each) = 12 pts Part ...10.2A Angles Formed by Two Straight Lines and a Transversal In the figure, a straight line EF intersects two other straight lines AB and CD. The straight line EF is called a transversal of AB and CD. The 8 angles formed are named according to their relative positions. Corresponding Angles Alternate Angles Interior Angles on the Same Side 1. STANDARD G.CO.C.9. GEO. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. Title: geo_3.3_proofs0001.pdf Author: JBRESLOW Created Date: 10/21/2014 1:41:45 PM Parallel lines proving geometryParallel line proofs by kim tallud Geometry 2-2: proving lines parallelParallel proofs lesson. Geometry parallel lines proofs proof mathbitsnotebook practice involvingParallel lines proof geometry math them Parallel proofs line anglesParallel proofs lines. Check Details. Parallel lines proofs worksheet answersThis worksheet on geometry of straight lines for grade 9 covers the basics of geometry, including. vertically opposite angles. supplementary. and complementary angles. parallel lines which include. alternating angles, corresponding angles and. co-interior angles. and perpendicular lines.

Classify an angle as acute, obtuse, right, or straight. Understand and apply the Angle Addition Postulate. Use algebra to find missing measures of angles. Identify and use angle relationships including vertical angles, linear pair, adjacent angles, congruent angles, complementary angles, and supplementary angles.Free Geometry worksheets created with Infinite Geometry. Printable in convenient PDF format. Kuta Software. Open main menu. Products ... Proving lines parallel;contributed. Parallel lines are lines in a plane which do not intersect. Like adjacent lanes on a straight highway, two parallel lines face in the same direction, continuing on and on and never meeting each other. In the figure in the first section below, the two lines \overleftrightarrow {AB} AB and \overleftrightarrow {CD} C D are parallel.Parallel lines proving geometryParallel line proofs by kim tallud Geometry 2-2: proving lines parallelParallel proofs lesson. Geometry parallel lines proofs proof mathbitsnotebook practice involvingParallel lines proof geometry math them Parallel proofs line anglesParallel proofs lines. Check Details. Parallel lines proofs worksheet answersAlgebra I Worksheets Honors Geometry Honors Geometry Notes Honors Geometry Worksheets ... 3.4_proofs_with_perpendicular_lines.pdf: File Size: 200 kb: File Type: pdf: ... File Size: 116 kb: File Type: pdf: Download File. parallel_lines_poster_directions.pdf: File Size: 425 kb: File Type: pdf: Download File. 5.1_angles_of_triangles.pdf: File Size ...Displaying 8 worksheets for Proofs Parallel Lines. Worksheets are Using parallel lines in proofs, Proofs with parallel lines, Honors geometry chapter ...

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Here is a range of free geometry worksheets for 3rd graders. Using these sheets will help your child to: recognize and identify a range of 2d and 3d shapes; recognise and identify right angles and lines of symmetry; recognise and identify parallel lines; identify the faces, edges and vertices of 3d shapes; All the third grade geometry sheets in ...Title: geo_3.3_proofs0001.pdf Author: JBRESLOW Created Date: 10/21/2014 1:41:45 PMSTANDARD G.CO.C.9. GEO. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.Section 3.2 Parallel Lines and Transversals 133 Using Properties of Parallel Lines Find the value of x. a b 4 115° (x + 5)°SOLUTION By the Vertical Angles Congruence Theorem (Theorem 2.6), m∠4 = 115°.Lines a and b are parallel, so you can use the theorems about parallel lines. m∠4 + (x + 5)° = 180° Consecutive Interior Angles Theorem 115° + (x + …25) Fill in the blank so that the lines are not parallel: Line A goes through Line B goes through----- -----( , ) and ( , ) ( , ) and ( , ) Anything but 26) Write the equations of five lines that are parallel to y x Many answers. Ex: y x -2-Create your own worksheets like this one with Infinite Geometry. Free trial available at KutaSoftware.com In this worksheet, students complete two proofs. Each proof involves two parallel lines and a transversal. This worksheet is designed for high school students. Get Worksheet. Topics: Angles, Geometry. Grades: High School.

Proofs Parallel Lines - Displaying top 8 worksheets found for this concept.. Some of the worksheets for this concept are Using parallel lines in proofs, Proofs with parallel lines, Honors geometry chapter 3 proofs involving parallel and, Parallel lines proof work, Parallel lines and transversals work write all the, 3 parallel and perpendicular lines, Geometry beginning proofs packet 1, Unit 4 ... Lines and angles worksheets are perfect for students to learn and practice various problems about different angle concepts and situations. These worksheets are a great resource for students who wish to grow and improve their skills in angles. Lines and angles worksheets consist of concepts like naming angles, lines, classifying angles ...Pairs of Angles. When parallel lines get crossed by another line (which is called a Transversal ), you can see that many angles are the same, as in this example: These angles can be made into pairs of angles which have special names. Click on each name to see it highlighted: Now play with it here. Try dragging the points, and choosing different ...50°. 63°. 7. −7. 6. 12. 8. 18) Even if the lines in question #16 were not. Any value other than 8. Ideally 0 ≤ x ≤ 10. parallel, could. No, that would make the angles 189° and 206°. Create your own worksheets like this one with Infinite Geometry. Free trial available at KutaSoftware.com.This curriculum is divided into the following units: Unit 1 – Geometry Basics. Unit 2 – Logic & Proof. Unit 3 – Parallel & Perpendicular Lines. Unit 4 – Congruent Triangles. Unit 5 – Relationships in Triangles. Unit 6 – Similar Triangles. Unit 7 – Right Triangles & Trigonometry. Unit 8 – Polygons & Quadrilaterals.3 Parallel and Perpendicular Lines 3.1 Pairs of Lines and Angles 3.2 Parallel Lines and Transversals 3.3 Proofs with Parallel Lines 3.4 Proofs with Perpendicular Lines 3.5 Equations of Parallel and Perpendicular Lines Tree House (p. 130) Kiteboarding (p. 143) Crosswalk (p. 154) Bike Path (p. 161) Gymnastics (p. 130) Bike Path (p. 161) Kiteboarding3.3 - Proofs with Parallel Lines. Common Core State Standards: HSG-CO.C.9, HSG-CO.D.12. Expected Learning Outcomes. The students will be able to: 1) Prove that two or more lines are parallel.10.2A Angles Formed by Two Straight Lines and a Transversal In the figure, a straight line EF intersects two other straight lines AB and CD. The straight line EF is called a transversal of AB and CD. The 8 angles formed are named according to their relative positions. Corresponding Angles Alternate Angles Interior Angles on the Same Side 1.Parallel lines proofs worksheet answers / proving lines parallel 13 3 proving lines parallel worksheet answers — db-excel.com Parallel line proofs worksheetParallel lines worksheet proofs answers proving activity proof geometry chessmuseum school high teacherspayteachers related posts.Step 1: Read through the steps of the proof, making note of the given information (usually in "Step 1") and what it is we are asked to prove (usually in the last "Step"). Step 2: Identify which ... Proving Lines Parallel Vertical angles are . NMP QPR QPR PRQ NMP Transitive Property of Congruence PRQ If 2 lines are cut by a transversal such that alt. int. ’s are , the lines are ǁ. m C + m D = 180° If 2 lines are cut by a transversal such that cons. int. ’s are supp., the lines are ǁ.

PROVING LINES ARE PARALLEL WORKSHEET. Problem 1 : In the diagram given below, if ∠1 ≅ ∠2, then prove m||n. Problem 2 : In the diagram given below, if ∠4 and ∠5 are supplementary, then prove g||h. Problem 3 : In the diagram given below, find the value of x that makes j||k.

The purchase of these items, accompanied by the materials on the site, will provide you with a smooth year of teaching. This page is the high school geometry common core curriculum support center for objective G.CO.9 about proving theorems about lines and angles. Many teaching resources such as activities and worksheets are provided here.SaaS small businesses are facing challenging macroeconomic conditions once again. Here are 5 tips for recession-proofing your SMB. SaaS small businesses are facing challenging macr...complementary), then the lines are parallel. 3. If two lines are cut by a transversal so that (alternate interior, alternate exterior, corresponding) angles are congruent, then the lines are parallel. 4. If two coplanar lines are perpendicular to the same line, then the two lines are (perpendicular, parallel, skew) to each other. a || b. State ...Download this free debt snowball worksheet that will tell you exactly how many months until you are debt free once you fill it out. The Debt Snowball, made famous for being part of...How to use two column proofs in Geometry, Practice writing two column proofs, How to use two column proof to prove parallel lines, perpendicular lines, Grade 9 Geometry, prove properties of kite, parallelogram, rhombus, rectangle, prove the Isosceles Triangle Theorem, prove the Exterior Angle Theorem, with video lessons, examples and step-by-step solutions. Proving Lines Parallel 134 Chapter 3 Parallel and Perpendicular Lines page 30 and Lesson 2-1 Algebra Solve each equation. 1. 2x +5 =27 11 2. 8a-12 =20 4 3. x-30 +4x +80 =180 26 4. 9x-7 =3x +29 6 Write the converse of each conditional statement. Determine the truth value of the converse. 5–6. See back of book. 5. If a triangle is a right ... Hand over this set of worksheets on Parallel and Perpendicular Lines to your students for teaching them to identify, draw and determine parallel and perpendicular lines. In addition to this, the set also contains practice worksheets on determining whether two lines are parallel or perpendicular, using points, slopes and equations.A series of free, online High School Geometry Video Lessons and solutions. Videos, worksheets, and activities to help Geometry students. In this lesson, we will learn. alternate interior angles. alternate exterior angles. same side interior and same side exterior angles. converse of the parallel lines theorem.Discover the power of consumer reviews as we break down the importance of social proof and its role in customer referrals in this post. Trusted by business builders worldwide, the ...congruent, then the lines are parallel. Notes: Consecutive Interior Angles Converse If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel. Notes: If two lines are parallel to the same line, then they are parallel to each other. Notes: k 5 4 j k j 1 8 3 j 5 p q r jk j k If ∠∠3 ...

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Geometry (all content) 17 units · 180 skills. Unit 1 Lines. Unit 2 Angles. Unit 3 Shapes. Unit 4 Triangles. Unit 5 Quadrilaterals. Unit 6 Coordinate plane. Unit 7 Area and perimeter. Unit 8 Volume and surface area.Download this free debt snowball worksheet that will tell you exactly how many months until you are debt free once you fill it out. The Debt Snowball, made famous for being part of...Parallel Lines and Proofs. Name: ____________________________________. Copyright © 2014 k12mathworksheets.com. All Rights Reserved. Free for educational use at home …Created Date: 1/26/2014 2:23:54 PMwith multiple lines, systems of equations and factoring! (we had 2 worksheets on this!) 3.3 Proving Lines Parallel **Converses used to show lines are PARALLEL Corresponding Angles Converse Alternate Interior Angles Converse Alternate Exterior Angles Converse Consecutive Interior- (Same Side Interior) Angles Converse Transitive Property of ...Unit 6: Analytic geometry. 0/1000 Mastery points. Distance and midpoints Dividing line segments Problem solving with distance on the coordinate plane. Parallel & perpendicular lines on the coordinate plane Equations of parallel & perpendicular lines.Parallel lines are seen in many common 2D shapes. For example, Each side of a square is made of a line segment that is part of a line. The opposite sides of a square are parallel. There are also many examples of parallel lines in real life. For example, The lines that pass by the sides of a table top are parallel.Infinite Geometry. Infinite Algebra 2. Infinite Precalculus. Infinite Calculus. Buy Online Purchase Orders Renewals. ... Free Worksheets Infinite Pre-Algebra Infinite Algebra 1 Infinite Geometry Infinite Algebra 2 Infinite Precalculus Infinite Calculus. Buy. Online Purchase Orders Renewals.Proving Lines Parallel Vertical angles are . NMP QPR QPR PRQ NMP Transitive Property of Congruence PRQ If 2 lines are cut by a transversal such that alt. int. ’s are , the lines are ǁ. m C + m D = 180° If 2 lines are cut by a transversal such that … ….

Parallel, Perpendicular and Intersecting Lines Worksheets. This module deals with parallel, perpendicular and intersecting lines. A variety of pdf exercises and word problems will help improve the skills of students in grade 3 through grade 8 to identify and differentiate between parallel, perpendicular and intersecting lines.The first one focuses on angles, the second on lines and angles. The third one puts it all together. Homework 1 - We can see that ∠ABD and ∠CBD form a linear pair, so they are supplementary to each other. Homework 2 - Vertical angles are equal is the lead here. Homework 3 - Knowing that two lines are parallel, you can learn a lot.Parallel Lines and Proofs. Name: ____________________________________. Copyright © 2014 k12mathworksheets.com. All Rights Reserved. Free for educational use at home …This is part of our collection of Short Problems. You may also be interested in our longer problems on Angles, Polygons and Geometrical Proof Age 11-14 and Age 14-16. Printable worksheets containing selections of these problems are available here: Stage 3 … Pairs of Angles. When parallel lines get crossed by another line (which is called a Transversal ), you can see that many angles are the same, as in this example: These angles can be made into pairs of angles which have special names. Click on each name to see it highlighted: Now play with it here. Try dragging the points, and choosing different ... Displaying all worksheets related to - Proofs Parallel Lines. Worksheets are Using parallel lines in proofs, Proofs with parallel lines, Honors geometry chapter 3 proofs involving parallel and, Parallel lines proof work, Parallel lines and transversals work write all the, 3 parallel and perpendicular lines, Geometry beginning proofs packet 1, Unit 4 …When a transversal crosses parallel lines, same-side interior angles are congruent. Angles that form a linear pair are supplementary. Angles that form a linear pair are supplementary. Vertical angles are congruent. Vertical angles are congruent. Learn for free about math, art, computer programming, economics, physics, chemistry, biology ...Unit test. Level up on all the skills in this unit and collect up to 1,900 Mastery points! In this topic, we'll learn about special angles, such as angles between intersecting lines and triangle angles. Next, we'll learn about the Pythagorean theorem. Finally, we'll find volume of curved 3D shapes like spheres, cones, and cylinders.But "investors would like to see a more sustained period of policy certainty before they can begin to feel more confident again," an analyst says. In the past year, it’s been almos... Geometry parallel lines proofs worksheet, Displaying all worksheets related to - Proofs Parallel Lines. Worksheets are Using parallel lines in proofs, Proofs with parallel lines, Honors geometry chapter 3 proofs involving parallel and, Parallel lines proof work, Parallel lines and transversals work write all the, 3 parallel and perpendicular lines, Geometry beginning proofs packet 1, Unit 4 …, Practice Problems on Parallel Lines cut by trransversal and angles. Corresponding, alternate exterior, same side interior, Proving Lines Parallel Vertical angles are . NMP QPR QPR PRQ NMP Transitive Property of Congruence PRQ If 2 lines are cut by a transversal such that alt. int. ’s are , the lines are ǁ. m C + m D = 180° If 2 lines are cut by a transversal such that …, A flow proof is just one representational style for the logical steps that go into proving a theorem or other proposition; rather than progress downward in two columns, as traditio..., Proofs parallel lines worksheet geometry worksheetsParallel proofs involving Parallel lines proofs practice worksheet for 8thLines parallel proofs worksheet answers geometry honors school vintage high section chessmuseum transversal related posts. Check Details., 3.1 Identify Pairs of Lines/Angles Parallel Lines Parallel Postulate Perpendicular Postulate Skew Lines Parallel Planes Diagram with a cube/box Transversals Angles formed by transversals Corresponding Angles Alternate Interior Angles Alternate Exterior Angles Consecutive Interior- (Same Side Interior) Angles 3.2- Parallel Lines and Transversals, A flow proof is just one representational style for the logical steps that go into proving a theorem or other proposition; rather than progress downward in two columns, as traditio..., When a transversal crosses parallel lines, same-side interior angles are congruent. Angles that form a linear pair are supplementary. Angles that form a linear pair are supplementary. Vertical angles are congruent. Vertical angles are congruent. Learn for free about math, art, computer programming, economics, physics, chemistry, biology ... , 3.1 Identify Pairs of Lines/Angles Parallel Lines Parallel Postulate Perpendicular Postulate Skew Lines Parallel Planes Diagram with a cube/box Transversals Angles formed by transversals Corresponding Angles Alternate Interior Angles Alternate Exterior Angles Consecutive Interior- (Same Side Interior) Angles 3.2- Parallel Lines and Transversals, This free geometry worksheet requires the use of the properties of parallel lines including the Alternate Interior Angle Theorem, Corresponding Angles Theorem, and the Same-Side Interior Angle Theorem and their converses. Problems include the completion proofs and finding the values of missing angles to make a pair of lines parallel. To prove ... , Step 1: Read through the steps of the proof, making note of the given information (usually in "Step 1") and what it is we are asked to prove (usually in the last "Step"). Step 2: Identify which ..., Parallel lines are defined as the existence of two lines that will never intersect. ... Print Parallel Line Rules, Proofs & Examples Worksheet 1. If angle 2 measures 60, what does angle 8 measure ..., There are several angle relationships of which students should be aware. Complementary angles are two angles that together form a 90 degree angle; supplementary angles are two angles that together form a 180 degree angle; and explementary angles are two angles that together form a 360 degree angle.Vertical angles are found at line intersections; angles …, If two lines are perpendicular to the same line, they are parallel to each other and will never intersect. Advertisement Welders and carpenters use all sorts of tools to set things..., Geometry / Trig 2 Name _____ 3.2 Parallel Lines & Proofs Practice Date _____ 1 2 3 l m t 1 2 3 l m t Proof #3 Given: k || l Prove: 1 is supplementary to 7 1. _____ 2. If lines are parallel, then alternate interior angles are congruent. 3. Angle Addition Postulate 4. Substitution 5. _____ Statements 1 2 7 k l t, In geometry, parallel lines are the lines that do not meet in a plane. Two straight lines are said to be parallel if they do not intersect at any point in a plane. If two lines have a third …, 👉 Learn how to write a proof when given angles from parallel lines and a transversalWe will explore angle relationships with parallel lines and a transversa..., Free Geometry worksheets created with Infinite Geometry. Printable in convenient PDF format. Kuta Software. Open main menu. Products ... Proving lines parallel; , complementary), then the lines are parallel. 3. If two lines are cut by a transversal so that (alternate interior, alternate exterior, corresponding) angles are congruent, then the lines are parallel. 4. If two coplanar lines are perpendicular to the same line, then the two lines are (perpendicular, parallel, skew) to each other. a || b. State ..., Parallel lines are defined as the existence of two lines that will never intersect. ... Print Parallel Line Rules, Proofs & Examples Worksheet 1. If angle 2 measures 60, what does angle 8 measure ..., Quiz & Worksheet Goals. To demonstrate your competence of parallel lines, you will be quizzed on the following: Angles (corresponding, supplementary, alternate interior, and alternate exterior ..., Triangle And Parallel Lines. Displaying all worksheets related to - Triangle And Parallel Lines. Worksheets are 7 proportional parts in triangles and parallel lines, Name geometry unit 2 note packet triangle proofs, Geometry part 1 lines and angles, Ms work 132 153 geometry 06, Parallel lines parallel, Proving lines parallel, Parallel ..., parallel lines and transversals -Prove that two lines are parallel Worksheet 3.2 -3.3 3 3.4 Find and Use Slopes of Lines -Find slopes of lines -Use slopes to identify parallel and perpendicular lines Worksheet 3.1 -3.4 Study for Quiz 4 QUIZ 3.1-3.4 3.5 Write and Graph Equations of Lines -Demonstrate mastery -Wr ite equations of lines in, Geometry: Proofs and Postulates Worksheet Practice Exercises (w/ Solutions) Topics include triangle characteristics, quadrilaterals, circles, midpoints, SAS, and more. Mathplane.com, Implementing the right tools and systems can make a huge impact on your business. Below are expert tips and tools to recession-proof your business. Implementing the right tools and..., Sep 5, 2015 - Worksheet of proofs for parallel lines cut by a transversal. Students will practice using theorems about parallel lines, including Alternate Interior Angles Theorem, Alternate Exterior Angles Theorem, Corresponding Angles Postulate, Consecutive Interior Angles Theorem, as well as Linear Pair Postul..., Parallel Lines Proofs. 1. Multiple Choice. The last statement is <4 = <6. What is the last reason. 2. Multiple Choice. Which is the correct reason for statements 2 and 4 in the proof?, Infinite Geometry. Infinite Algebra 2. Infinite Precalculus. Infinite Calculus. Buy Online Purchase Orders Renewals. ... Free Worksheets Infinite Pre-Algebra Infinite Algebra 1 Infinite Geometry Infinite Algebra 2 Infinite Precalculus Infinite Calculus. Buy. Online Purchase Orders Renewals., Printer marks are the lines that appear in the corner or sides of documents. Print shops use these marks to make sure different color proofs are properly lined up and to indicate w..., Proving Lines Parallel Vertical angles are . NMP QPR QPR PRQ NMP Transitive Property of Congruence PRQ If 2 lines are cut by a transversal such that alt. int. ’s are , the lines are ǁ. m C + m D = 180° If 2 lines are cut by a transversal such that cons. int. ’s are supp., the lines are ǁ. , 10.2A Angles Formed by Two Straight Lines and a Transversal In the figure, a straight line EF intersects two other straight lines AB and CD. The straight line EF is called a transversal of AB and CD. The 8 angles formed are named according to their relative positions. Corresponding Angles Alternate Angles Interior Angles on the Same Side 1., The red angles below are alternate exterior ones, they are equal.. This allows us to use the supplementary angles that measure (2x) and (3x+15) to set up the equation below.. 2x+ 3x+15 = 180 5x + 15 = 180 5x = 165 x = $$ \frac{165}{5} = 33 $$, 4.9. (8) $1.50. PDF. There are 7 practice proofs for parallel lines, ranging in difficulty from 3 steps to 8 steps. The proofs also include practice with the Theorem "If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line."